Shawnje Granville
Benjamin Banneker Academy
January 17,2013
Trigonometry
TRIGANOMETRY
The history of algebra goes way back in time (more than 4000 years . Algebra is a sub within mathematics, but for historical reasons, the word "algebra" has three meanings that can all suffice in defining the word or term . Algebra can mean use of letters and symbols to represent values and their relations, especially for solving equations,major branch of mathematics which studies relations and operations or mathematical structure as a "linear" ring, is also called "algebra," or sometimes .algebra is one of main branches of pure mathematics, together with geometry, analysis, topology,statistics and number theory.
Algebra s often taught from anywhere between secondary school to the 12th grade . But does anyone ever stop to wonder were it originated ? Historians trace the roots of algebra back to ancient Babylon society , they developed the first arithmetic mathematical system .It is believed that priests used mathematics and algebra along side their religious rituals. in the 1st millennium BC, mathematicians usually solved such equations by geometric methods, such as those described in the Rhind Mathematical Papyrus, Euclid's Elements, and The Nine Chapters on the Mathematical Art. Much of our knowledge of ancient Egyptian mathematics, including algebra, is based on the Rhind papyrus. This was written about 1650 B.C. The Greek mathematician Diophantus has traditionally been known as the "father of algebra" but in more recent times there is debate over whether alKhwarizmi, who created the discipline of “aljabr“, should be considered the “father of algebra “.The Persian mathematician Omar Khayyam is credited with identifying the foundations of algebraic geometry and found the general geometric solution of the cubic equation. With influences and theories from all these different people the renowned math principle used in schools all over his world was...
...The ancient Nubians used a similar methodology.[5] The ancient Greeks transformed trigonometry into an ordered science.[6]
Classical Greek mathematicians (such as Euclid and Archimedes) studied the properties of chords and inscribed angles in circles, and proved theorems that are equivalent to modern trigonometric formulae, although they presented them geometrically rather than algebraically. Claudius Ptolemy expanded upon Hipparchus' Chords in a Circle in his Almagest.[7] The modern sine function was first defined in the Surya Siddhanta, and its properties were further documented by the 5th century Indian mathematician and astronomer Aryabhata.[8] These Greek and Indian works were translated and expanded by medieval Islamic mathematicians. By the 10th century, Islamic mathematicians were using all six trigonometric functions, had tabulated their values, and were applying them to problems in spherical geometry.[citation needed] At about the same time, Chinese mathematicians developed trigonometry independently, although it was not a major field of study for them. Knowledge of trigonometric functions and methods reached Europe via Latin translations of the works of Persian and Arabic astronomers such as Al Battani and Nasir alDin alTusi.[9] One of the earliest works on trigonometry by a European mathematician is De Triangulis by the 15th century German mathematician Regiomontanus. Trigonometry was still so little...
...f ter
A Brief History of Trigonometry
A painting of the famous greek geometrist, and "father of measurement", Euclid. In the times of the greeks, trigonometry and geometry were important mathematical principles used in building, agriculture and education.
The Babylonians could measure angles, and are believed to have invented the division of the cirle into 360º.[1] However, it was the Greeks who are seen as the original pioneers of trigonometry.
A Greek mathematician, Euclid, who lived around 300 BC was an important figure in geometry and trigonometry. He is most renowned for Euclid's Elements, a very careful study in proving more complex geometric properties from simpler principles. Although there is some doubt about the originality of the concepts contained within Elements, there is no doubt that his works have been hugely influential in how we think about proofs and geometry today; indeed, it has been said that the Elements have "exercised an influence upon the human mind greater than that of any other work except the Bible.<Complete Dictionary of Scientific Biography, 2008>

[edit]First Tables of Sines or Cosines
Hiparchus
In the second century BC a Greek mathematician, Hipparchus, is thought to have been the first person to produce a table for solving a triangle's lengths and...
...Running Head: History of TrigonometryHistory of Trigonometry
Rome Fiedler
History of Mathematics 501
University of Akron
April 29, 2012
History of Trigonometry: An Introduction
Trigonometry is useful in our world. By exploring where these concepts come from provides an understanding in putting this mathematics to use. The termTrigonometry comes from the Greek word trigon, meaning triangle and the Greek word meatria meaning measurement. However it is not native to Greek in origin. The mathematics comes from multiple people over a span of thousands of years and has touched over every major civilization. It is a combination of geometry, and astronomy and has many practical applications over history.
Trigonometry is a branch of math first created by 2nd century BC by the Greek mathematician Hipparchus. The history of trigonometry and of trigonometric functions sticks to the general lines of the history of math.
Early research of triangles could be found in the 2nd millennium BC, in Egyptian and Babylonian math. Methodical research of trigonometric functions started in Greek math, and it reached India as part of Greek astronomy. In Indian astronomy, the research of trigonometric...
...Trigonometry (from Greek trigōnon "triangle" + metron "measure"[1]) is a branch of mathematics that studies triangles and the relationships between the lengths of their sides and the angles between those sides. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclical phenomena, such as waves. The field evolved during the third century BC as a branch of geometry used extensively for astronomical studies.[2] It is also the foundation of the practical art of surveying.
Trigonometry basics are often taught in school either as a separate course or as part of a precalculus course. The trigonometric functions are pervasive in parts of pure mathematics and applied mathematics such as Fourier analysis and the wave equation, which are in turn essential to many branches of science and technology. Spherical trigonometry studies triangles on spheres, surfaces of constant positive curvature, in elliptic geometry. It is fundamental to astronomy and navigation. Trigonometry on surfaces of negative curvature is part of Hyperbolic geometry.
Contents
f one angle of a triangle is 90 degrees and one of the other angles is known, the third is thereby fixed, because the three angles of any triangle add up to 180 degrees. The two acute angles therefore add up to 90 degrees: they are complementary angles. The shape of a triangle is completely determined,...
...Paper  I
1. Sources: Archaeological sources:Exploration, excavation, epigraphy, numismatics, monuments Literary sources: Indigenous: Primary and secondary; poetry, scientific literature, literature, literature in regional languages, religious literature. Foreign accounts: Greek, Chinese and Arab writers.
2. Prehistory and Protohistory: Geographical factors; hunting and gathering (paleolithic and mesolithic); Beginning of agriculture (neolithic and chalcolithic).
3. Indus Valley Civilization: Origin, date, extent, characteristics, decline, survival and significance, art and architecture.
4. Megalithic Cultures: Distribution of pastoral and farming cultures outside the Indus, Development of community life, Settlements, Development of agriculture, Crafts, Pottery, and Iron industry.
5. Aryans and Vedic Period: Expansions of Aryans in India. Vedic Period: Religious and philosophic literature; Transformation from Rig Vedic period to the later Vedic period; Political, social and economical life; Significance of the Vedic Age; Evolution of Monarchy and Varna system.
6. Period of Mahajanapadas: Formation of States (Mahajanapada): Republics and monarchies; Rise of urban centres; Trade routes; Economic growth; Introduction of coinage; Spread of Jainism and Buddhism; Rise of Magadha and Nandas. Iranian and Macedonian invasions and their impact.
7. Mauryan Empire: Foundation of the Mauryan Empire, Chandragupta, Kautilya and Arthashastra; Ashoka;...
...Teaching trigonometry using Empirical Modelling
0303417
Abstract
The trigonometric functions sin(x), cos(x) and tan(x) are relationships that exist between the angles
and length of sides in a rightangled triangle. In Empirical Modelling terms, the angles in a triangle
and the length of the sides are observables, and the functions that connect them are the definitions.
These welldefined geometric relationships can be useful when teaching GCSElevel students about
the functions, as they provide a way to visualise what can be thought of as fairly abstract functions.
This paper looks at how different learning styles apply to Empirical Modelling, and presents a practical example of their use in a model to teach trigonometry.
1 Introduction
The trigonometric functions sin(x), cos(x) and tan(x)
are relationships that exist between the angles and
length of sides in a rightangled triangle. In Empirical Modelling terms, the angles in a triangle and the
length of the sides are observables, and the functions
that connect them are the definitions. These welldefined geometric relationships can be useful when
teaching GCSElevel students about the functions,
as they provide a way to visualise what can be
thought of as fairly abstract functions. Rather than
teaching students by showing them diagrams in an
instructive way (already a good way of doing it), a
constructive approach may allow students to gain a
better understanding...
...Trigonometry (from Greek trigōnon "triangle" + metron"measure"[1]) is a branch of mathematics that studies triangles and the relationships between their sides and the angles between these sides. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclical phenomena, such as waves. The field evolved during the third century BC as a branch of geometry used extensively for astronomical studies.[2] It is also the foundation of the practical art of surveying.
Trigonometry basics are often taught in school either as a separate course or as part of a precalculus course. The trigonometric functions are pervasive in parts of pure mathematics and applied mathematics such as Fourier analysis and the wave equation, which are in turn essential to many branches of science and technology. Spherical trigonometry studies triangles on spheres, surfaces of constant positive curvature, in elliptic geometry. It is fundamental to astronomy and navigation. Trigonometry on surfaces of negative curvature is part of Hyperbolic geometry.


\History
Main article: History of trigonometry
The first trigonometric tablewas apparently compiled byHipparchus, who is now consequently known as "the father of trigonometry."[3]
Sumerian astronomers introduced angle...
...more than a man who lived a very powerless and negative life, getting his hands on a small
amount of power in a small antisemitic party and going on a power trip resulting in being the
worlds most infamous leader.
To live the childhood that HItler lived wouldn’t be easy for anyone. Neglect, negativity
and powerlessness surrounded him everyday of his life until he moved to Germany in 1913.
When he moved he noticed opportunities opening up. A chance for him to gain power, to show
that he could do something in this world instead of living on the streets, he was going to live big.
Hitler was determined to live with his self depicted aryan race, along side power and wealth.
Through investigation of Hitlers psychiatric history its also clear to see that Hitler had not
one, but many mental issues.
Dr. Ian Kershaw, a history professor at the University of Sheffield
in England, wrote a biography that goes into great depth and investigation of Hitler's mental
health. Also, Dr. Fritz Redlich, a neurologist and psychiatrist, concluded that Hitler exhibited
many psychiatric symptoms, including extreme paranoia and defenses that ''could fill a
psychiatry textbook.” Hitler is also reported of having extreme O.C.D, washing his hands
obsessively. Hitler is also said to have an extreme addiction to nicotine, doing anything in his
power to have it at all times and becoming very angry and short tempered when he did not
have it.
Adolf Hitler is without...
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